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In this paper, we discuss an hp-discontinuous Galerkin finite
element method (hp-DGFEM) for the laser surface hardening of
steel, which is a constrained optimal control problem governed by a
system of differential equations, consisting of an ordinary
differential equation for austenite formation and a semi-linear
parabolic differential equation for temperature evolution. The space
discretization of the state variable is done using an hp-DGFEM,
time and control discretizations are based on a discontinuous
Galerkin...
In this paper, we discuss an hp-discontinuous Galerkin finite
element method (hp-DGFEM) for the laser surface hardening of
steel, which is a constrained optimal control problem governed by a
system of differential equations, consisting of an ordinary
differential equation for austenite formation and a semi-linear
parabolic differential equation for temperature evolution. The space
discretization of the state variable is done using an hp-DGFEM,
time and control discretizations are based on a discontinuous
Galerkin...
Given a nonempty convex set in a locally convex Hausdorff topological vector space, a nonempty set and two set-valued mappings , we prove that under suitable conditions one can find an which is simultaneously a fixed point for and a common point for the family of values of . Applying our intersection theorem we establish a common fixed point theorem, a saddle point theorem, as well as existence results for the solutions of some equilibrium and complementarity problems.
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